Computing device



Jan. 21, 1941. SMILEY COMPUTING DEVI-CE Filed'Feb. 19, 1938 2 Sheets-Sheet l Crib? 2:3

FIG RE 2 GIL'BEKT sHI LEY INVENTORQ ATTORNEY.

Jan. 21, 1941. gy 2,229,479

COMPUTING DEVICE Filed Feb. 19 1958 2 Sheets-Sheet 2 GILBERT SMILEY INVENTOR.

ATTORNEY.

Patented Jan. 21, I

UNITED STATES PATENT OFFICE 2,229,479 oomru'rmc. nnvr cn Gilbert Smiley, Hingham, Mass.

Application February 19, 1938, sci-n1 No. 191,409

5 Claims. (01. 235-84) v The present invention relates to a means and Through the application of depth of focus prinmethod of accurately determining lens adjustciples the subject may be clearly portrayed, while ment for cameras and the like to obtain maxithe background is sufiiciently blurred to obscure mum allowable depth of focus under general and distracting and unwanted details. Furthermore,

5 special operating conditions. the practice of subordinating extraneous details 5 In the formation of a latent photographic by blurring, while the subject is sharply portrayed image upon a light sensitive medium by the acoften introduces an apparent third, or depth, tion of a properly corrected lens, only that pordimension to an otherwise two dimensional piction of the subject upon which the lens is acture; often a valuable ability. In all these incurately focused will produce an image free from stances, and in others, a rapid, simple and sufm blur, sharply and clearly defined. Objects either ficiently accurate means of securing the necsbefore or behind the plane of focus will exhibit sary information as to the proper stop reprogressive blurring in the image; the degree of quired for a given depth of focus is of great blur or dispersion (lack of sharpness) increasvalue to the photographer.

l5 ing as the distance from the plane of "accurate To this end certain existing cameras are focus increases. Since a certain degree of blur equipped with depth of focus tables in which can be tolerated, and since blurring of images the limits of the depth of focus are'tabulated, of objects but slightly before or behind the plane versus the distance to the plane of accurate foof sharp focus is, in turn, very slight, there is a cus and the apertu t P 0f the lensother certain region related to the plane of accurate cameras are supplied with depth of focus scales 20 focus in which images of objects will be reprocoincident with the focusing means which autoduced with satisfactory (though not absolute) matically show the limits of focal dep for sharpness. This region is described as the focal ious stops at all settings within the range of depth, and as will be demonstrated, its limits the camera. In others, a small computing deare determined by the maximum permissible. vice is included, not connected with the focusing 25 amount of blurring, the focal length of the lens, means, but to be used in conjunction with such the relative aperture of the lens, and the dismeans. All these devices however, have a comtance from the optical centre of the lens to the mom factor-they are app y t the plane of accurate focus, all of which factors are l n r which y are mp r lly defined and illustrated in the ensuing text and the lens pl with h er on which hey 30 accompanying figures. are mounted, or with which they are supplied);

With a given lens focused for a given distance, My pr nt nv n n r s to a ep of the depth of focus may be increased by the acfocussing computing device which may readily tion of stopping down the lens. This action, be used with any lens suitable for focusing, and

which consists of utilizing only the more central which may be used by photographers having sev- 35 portion of the lens area, decreases the amount eral cameras and lenses, the device being equally of light passed in a unit of time through the lens applicable to all lenses regardless of focal length, opening, requiring a longer exposure for a given compensation for diiferences of focal length besubject of fixed illumination than would be reing made by means of a single simple adjustment.

ac quired were a larger portion of the lens area Furthermore my invention may readily and s im' 40 to be used. Since short exposures are normally ply be used with such special purpose lenses as desirable due to motion of the subject, the camfall into "wide-angle and telephoto classifiera or both, and since the practice of stopping cations as opposed to normal lenses used in gendown the lens to secure a greater depth of focus eral photography.

introduces an increase in required exposure time, My invention will be more readily understood 45 it is obvious that it is desirable to know the from the description in the specification below exact amount of stopping down required for a taken in connection with the drawings in whichgiven subject, in order that the exposure may be Figure 1 illustrates schematically the P kept at a minimum for the required depth of ples of the invention as applied to a simple double ,60 focus. However many photographic subjects convex object lens.

gain in artistic appeal. through the deliberate Figure 2 is a sectional view. of my computing application of depth of focus considerations to device, and, the problem in hand. Particularly on candid" Figure 31s a plan view looking downward from (imposed) portraiture, it is often impossible to the top of- Figure 2.

I select an artistic or desirable background. Figure 1 illultratesa photographic lens (shown as a simple double convex objective, which, it should be understood, is purely a simplified con struction, the complex structure of a highly corrected lens being too confusing for the purpose of analysis), sharply focused on an object plane at distance P from the lens center, producing an image on the image plane (film or plate) at distance Q from thelens center. It will be ob served that the bundles of light rays from points in front and rear planes (at distances P: and F1 from lens center, respectively) converge to points in two other image planes (at distances Q2 and Q1 from lens center, respectively), intersecting the film plane as circles of .diameter D. These circles are known as circles of confusion, and it has been arbitrarily determined that a circle of confusion one-one hundredth of an inch in diameter is entirely permissible in 8. normal eight inch by ten inch photographic print when viewed from a normal viewing distance (approximately three feet). Since many cameras produce a negative smaller in dimension than 8" by 10", it is obvious that the process of enlargement must be employed to secure a print of this size. Such enlargement imposes smaller limits on the permissible circle of confusion, which must be smaller in proportion to the degree of enlargement required.

All lenses have a constant factor known as focal length, for which the symbol F will hereafter he used. This factor is the distance between lens center and image plane with the lens focused on infinity. It is furthermore a com mon arbitrary practice to have the focal lemgth of the lens roughly equal to the diagonal of the negative covered by the lens, when the lens is to be used for general photography. It thus becomes apparent that negative dimensions are related to lens focal length and, since the til ameter of the permissible circle or contusion depends upon required enlargement (l. e. tive size) it is possible to relate the die-mete circle of confusion to the focal length of normal lens of the camera. illie term normal is here used to exclude special purpose lenses falling into wide-angle and "telephoto class? fisations. 7

Based on the reasonable assumption the average negative from a lens of tive focal length will require a ten diameter enlargement to produce an eight by ten inch print with one one-hundredth inch circle of confusion portion of the subject that is to he sharply portrayed, it becomes possible to derive the relationship between the maximum permissible circle of confusion diameter and the focal length of the normal lens. This relationship is a ratio, the numerical value of which is expressed by the factor A. From the foregoing:

It should be noted in the above formula that where an enlargement is to be made the allowable diameter of .the circle of confusion on the original negative must be divided by the enlargement power.

While the numerical value of 0.0005 is assigned to A in computing the scales of my invention,

I it should not be construed that my invention does not contemplate the use of other-values, nor is c ee es Another factor entering into the depth of focus computations is the relative aperture at which the lens is to be operated. This is defined as the ratlo of the focal length to the effective free diameter of the lens. For this ratio the symbol is used. Relative aperture may be expressed as follows:

With the foregoing factors in mind it is possible to proceed to the equation expressing j in terms of F, P1, P2, A. It can be demonstrated from the fundamental equation ill which is an exact relationship, fulfilling all requirements.

This derivation is set forth below.

Let 0, 91, and 02 respectively, be the angle subtended by the center line of the lens and the rays of light reflected from the greatest effective free diameter d, corresponding to the points P, P1 and P2, and intersecting the center line at the distances Q, Q1 and Q: respectively from the lens center. The plane embracing the point Q as in Figure l is the plane of the film. Then from Figure l D=2R and d=2r and Equa- Substituting in (c) Equation 3, however, may be closely approximated by- E 1 P2 A any: in which the term,

is neglected.

The error resulting in the diameter of the ultimate circle of confusion by this approximation is entirely negligible at normal working distances. The actual error is expressed by:

With, for example a lens of F=3", working at a focus of P=4=48", the error is but 6.67%, surely a permissible error at this short working distance. Since the error decreases rapidly with increased working distances, the usefulness of the device is not impaired by the slight error inherent in its generalized design.

Equation 4 may be rewritten:

cals of distances in logarithmic values and the scale a represents focal distances also calibrated in logarithmic functions. The disc has a pinrality of lines o thereon for correlating the scale :1 on the disc d with the scale a on the disc a. As indicated in Figure 3 by the special legends thereon, the scale a: at the left of disc a is the correction scale for special purpose lenses, while the scale I) on the disc b at the left and entitled F opposite the correction scale is the focal length scale of the lens. The c scale is provided with a setting mark which is located either for centimeter or inch use as denoted by cm. and in. respectively. Both scales F designated 1) and the spee cial purpose lens scale a: are focal length scales. At the right of the disc a, this disc overlaps the disc I: so that its edge lines coincide. This portion of the disc a is also provided with focal distance calibration and with a corresponding relative aperture, thereby of course setting relationship between the two elements. The special purpose scale is explained in the relationship just below. The intermediate disc 0 carries also the near point setting and there is likewise determined through the lines across this disc the far point setting as well.

It can also be demonstrated from the fundamental equation that- This will readily be seen from the similar rela- AEL- g P1 P2) tion derived above, namely 2 2P,P,-F P,+P, 2f Q: Q1Q Ql'FQ: P1 P1 since Q and P are conjugately related functions as illustrated from the derivation e from the fundamental equation above.

If, on the distance scale a point be located spaced midway between Prand P: (represented of course by their reciprocal values from Equation 6) that point will be found to locate P in accordance with Equation 7. This follows'directly from Equation 7 since from this equation P 2(P, P

From this may be derived the focus scale of my invention, Figure 2 and Flgure-3.

Because special purpose (wide-angle and telephoto) lenses have focal lengths unequal to the negative diagonal, their focal lengths 'cannot be used as a direct indication of the required degree of enlargement without compensation. It can be shown-in accordance with the previous equations relating to the circle of confusion that a focal length may be computed for setting purposes which will fulfill the requirements and yield a correct circle of confusion in accordance with the following equation:

where F is the focal length to be used in setting the computer. Fs is the focal length of the special purpose lens. F1: is the focal length of the normal lens for the camera. It may be shown from the above Equation 8 that where which is to say that the radius of the circle of confusion varies inversely as the aperture numher. Since the special pu pose lenses may be related to a normal lens for the camera in question by considering the ratio of the focal length of the special purpose lens (F) to the focal length of the normal lens (Fa) the stop correction equation may be derived first Z 10. ,,=E; from the above in which the subscript n denotes a normal lens.

Z 1 1. F, E

from 10 where subscript 3 denotes the special lens.

R, 5 12. n a

which denotes that the permissible circle of confusion for special purpose lens must vary inversely from the standard as the focal length of such varies from the standard or Since the disc c of Figures 2 and 3 already includes pose lenses. The equation for determining this setting is v centimeters (our) Near point (Pa)= l' Far point (Pi) =ae' Required: Relative aperture (f) and distance on which to focus (P) Frocedure: Line up scales as and b so that the numbers coincide because a normal lens is being employed. Set the b (F) scale to 3 inches. Set the near point arrow to .i feet on the distance scale d. Follow the aperture line opposite 5.4 feet on the distance scale back to the a (1;) scale and read the i value (f 16). Follow the aperture line from 16 on the focus a scale to the distance scale and read the focus value (4.6 feet) Case 2.Known: Normal lens of F=3" as above.

Focused on 4.4 feet Set at aperture i ll.

Required: Near point, (P2) and tar point (P1).

Procedure: Line up scales as and b as in Case 1, also set the F scale to 3". Set the aperture line from 11 on the focus scale to 4.4 feet on the distance scale. Read the near point on the distance scale opposite the near point arrow (4 feet). Read the far point opposite the aperture line from 11 on the a (1) scale (4.87 feet). In the use of special purpose lenses, the focal length of the special purpose lens on the 02 scale is set to the focal length of the normal lens in the same units (inches or centimeters) on the b (F) scale, and the focal length of the special purpose lens is then used in setting the b -(F) scale to the arrow on the scale.

For the purpose of deriving the simplified form of equation for computing the various scales, a complete mathematical analysis will be given.

The fundamental equation is expressed as These latter two equations illustrate the conjuportion of the lens) are y it.

assume and divergent, and it is these that form. the perimeter of the circle of confusion. They form an angle, 01, with the axis of the lens, the trigonometric tangent of which may be expressed as Q: thus;

6. tan 01 Q where r is the radius of the effective lens aperture and Q1 is the distance from lens center to plane of convergence tor rays from a point in the rearward plane (1?, from lens center). Furthermore it is possible to substitute for the following;

7. r=ga from the equation 9. tan 6 2 Since, at the intersection of two straight lines, opposite angles are equal, and since, also, tangents of equal angles are equal, it is possible to derive an equation for R, thus:

It now we wish to ascertain the value of P1,

the equation may be further manipulated:

A similar process may be applied to the determination of P2, the distance-to a forward plane, as illustrated in Figure 4. Thus:

14. tan 0P5;

l5. tan 0 2- from 14 and 7.

Equations 13 and 19 give the rearward and forward limits of local depth (Pi and P: respectively) in terms of focal setting, 1?, focal length, F, relative aperture, 1, and permissible radius of these variables as to rapidly determine missing factors in the following instances:

Known To determine l 9! P1! P F, P1, P: P. I

whereas the conventional depth of focus device only allows the following Known To determine and operates 101' but one value of F.

To design such a device further mathematical operations are necessary. They are:

20 Let =X 21. let g -x,

22. Let -X I 23. Let g- Y 24. Let Y.

25. Let Y,

26. Let =A Equation 26 introduces the variable factor which is brought about by the practice of photographic enlargement. Thus, if an image or 0.8 inch by 1.0 inch is to be enlarged some ten diameters to produce a photographic print 8 inches by 10 inches, it is obvious that the circle of confusion on the small image must be one tenth the diameter of the permissible circle of confusion on the enlarged print. Since the focal length, F, of a general pumose lens Varies approximately as the negative dimensions, the ratio term, A, accurately expresses the varying tolerance in image circle of confusion dimensions. Based on a 20 inch focal length lens for a direct 8 inch by 10 inch negative (requiring no enlargement) and a io th inch diameter circle of confusion, the factor A, for general purpose lenses becomes which is the factor used in computing the actual scales of my invention. This factor. however. may be changed without altering the essential nature of the invention.

To continue, it is necessary to get Equations 13 and 19 into such form that they may be used as scales on a computing means. The derivation follows:

Equations 33 and 37 are simplified forms of Equations 13 and 19, which permit the rlesign of suitable scales as the variable factors have been brought into proper relation for logarithmic manipulation. The simplification is mathematically exact throughout.

Logarithmic practice shows that, in division, the logarithm oi the result is equal to the difference of the logarithms of the two numbers involved. Thus: 7

where fln" is the accepted abbreviation for th natural or Naperian logarithm.

In the computation of natural logarithms, the expansion seriesmay he used. From Er-he Equation sill may he rewritten and, for all fairly large values of X, it may be demonstrated that the equation closely approximates the actual value, as the succeeding terms in Equation 41 do not materially affect the result for the larger values of X, such as are encountered in general (as opposed to specialized) photography.

Since it is evident that 43. InY= P from 20, 2

approximately, as detailed under 42 above.

Assuming, for example, a lens of F=l foot, a scale may readily be laid out as in Figure 3, proportionate to Followingis a condensed tabulation from which The distance scale, Equation 43, and the table accompanying Equation 43 must now he operated upon by another logarithmic scale proportional to in (liZAf) as in Equations 38 and 39. A warrantable approximation,

44. In (1+S) :5

may he used here, as it refers .to "S as a small quantit thus:

45. in (l-l-ZAI') =2Af when 2A) is small as contrasted with unity (1). Also, the logarithmic distance of (l-2Af) is the same (i. e.': 2A1) though in the opposite direction. Thus the logarithmic distance from Y1 to Y2 is 2(2Af) or 4A). Tabulated, this becomes :ZDX LA EICfilB 4A], in chem l 0310 02 'l. A1014 Q23 2 ill)- Gill 2. 8 @028 U5? .oil l'i .039 5. G .0843! ll? 8 01139 36 3 ll 0113 a 2215 i6 016G 320 22 0223 $62 82 0320 s 640 44 0453 .905 64 0640 i. 280 as W05 3. 810 128 1280 2 560 The slight disparity between the columns lies in the fact that camera stop values are approxlq mately proportional to 45 steps, the computations are exactly in such steps. The error introduced by the Equation 45 is so slight as to be negligible in the tabulation.

The sectional drawing in Figure 2 serves to illustrate one form of construction possible in the actual manufacture of my invention. The three top scale carrying members are quite firmly gripped by eyelet 1 which serves to create sufficient friction to maintain the focal setting and special purpose lens setting once suchsetting has been made. Eyelet e fastens lesstightly through eyelet f and the lower scale carrying member so that the distance scale may be rotated more freely, facilitating use.

While circular scales are illustrated in Figure 2 nothing in my invention precludes its application disclosed in Figure 2, should not be construed as limiting my invention as to mechanical form. Such improvements as the elimination of parallax by placing scales in the same plane, etc., are also contemplated.

Having now described my invention, I claim:

1. A depth of focus computing device for determining proper relationships between depth of focus, relative aperture openings and lens focal lengths, comprising a plurality of discs having means mounting them concentrically and together, said discs consisting of one disc having at one side thereof a scale of logarithmic callbrations corresponding to relative aperture openlugs and continuing at the other side thereof in a. similar scale of lens focal lengths, a second disc having a. scale of logarithmic calibrations of object distances and a third disc having a plurslity of lines correlating said first and last scales including a. near point setting for the object distance scale and a. zero point setting for the lens focal length scale whereby the near point and for point, the depth focus. the relative aperture opening and the mean focus may be determined.

2. A depth of focus computing device for de-' termining proper relationships between depth of focus, relative aperture openings and lens focal lengths, comprising separate means mounting a plurality of parallelscales, means for permitting moving of said scales parallel to each other, one of said separate means having a scale of logarithmic calibrations of object distances, the other of said means having logarithmic calibrations of relative aperture openings, and the same scale, repeated a definitely spaced position therefrom, as a scale of lens focal lengths and means mounting a third scale between the others having lines correlating the object distances with the aperture openings and indices marking the settings for the lens focal lengths and object distances.

3. A depth of focus computing device as set forth inclaim 2 having means mounting an additional similar lens focal length scale, movable parallel with respect to the first lens focal length scale and interposed between the first lens focal length scale and the index for marking the setting for the lens focal lengths.

4. A depth of focus computing device as set forth in claim 2 having the said scale of logarithmic calibrations of relative aperture openings also marked with focus lengths.

5. A depth of focus computing device as set forth in claim 2 having the said scale of logarithmic calibrations of relative aperture openings marked in corresponding focal lengths.

' GILBERT SMILEY. 

